Abstract
In this paper, we study various topological properties of generic smooth maps between manifolds whose regular fibers are disjoint unions of homotopy spheres. In particular, we show that if a closed 4 -manifold admits such a generic map into a surface,then it bounds a 5 -manifold with nice properties. As a corollary, we show that each regular fiber of such a generic map of the 4 -sphere into the plane is a homotopy ribbon 2 -link and that any spun 2 -knot of a classical knot can be realized as a component of a regular fiber of such a map.
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